$59.99
Taxes may apply at checkout.
Elements of Functional Analysis
From Banach Spaces to Elliptic Problems
Functional analysis
can be understood as a shift, within mathematical analysis, from the study of individual functions to the study of function spaces, their structures, and the mappings between them. Developed primarily during the 20th century, this theory continues to be essential for the study of partial differential equations.
This textbook begins with the general theory
Banach spaces, Hilbert spaces, and the spectral theory of operators. It then proceeds to a thorough account of Schwartz’s Theory of Distributions and some of its applications, such as the fundamental solutions of classical operators in physics, the Malgrange–Ehrenpreis Theorem, hypoelliptic operators, and the Schrödinger equation.
An extensive chapter is dedicated to the study of Sobolev spaces
including functions of bounded variation. These spaces provide the appropriate framework for the study of elliptic boundary value problems, which form the focus of the final chapter.
Drawing on years of teaching experience
this textbook is ideal for introductory graduate courses, featuring historical notes and numerous exercises that reinforce learning and complement the core material.
